On Algebraic Structure of L-Fuzzy Bags

Abstract

This study introduces a revised definition for fuzzy bags. It is based on the definition of bags given by Delgado et al. (Int J Intell Syst 2009;24:706–721) in which each bag has two parts: function and summary information. The new definition is given as a special case of L‐fuzzy bags, where L is a complete lattice. By some examples, the new concept is illustrated. Furthermore, the algebraic structure of L‐fuzzy bags is studied and the concept of α‐cuts, L‐fuzzy bag relations, and related theorems are given.

A Note on L-Fuzzy Bags and Their Expected Values

“…In the next section, we review the concept of fuzzy bags and quote some results about them. For more details see [7] and [8].…”

“…As it is shown in [5], the lattice of all fuzzy bags defined by D e l g a d o et al [2] is a complete Boolean algebra which is not compatible with the nature of fuzziness. Improving this incompatibility, in the present paper, we quote a revised definition of fuzzy bags as a special case of L-fuzzy bags based on the proposed definition of bags in [2].…”

“…[8])º In the case that L = [0, 1], the defined L-fuzzy bag in Definition 4 is called fuzzy bag.Here, the concept of L-fuzzy bag is illustrated by an example.Example 2 ([8]). Let L = [0, 1], O = {Ben, Sue, Tom, John, Stan, Bill, Kim, Ana, Sara} and P = {young, middle age, old} is the set of some linguistic descriptions of age.…”

Parameters of Fuzzy Bags

“…Then, they proposed new definitions for bags and fuzzy bags. As it is shown in [3], the lattice of all fuzzy bags defined by Delgado et al [2] is a complete Boolean algebra which is not compatible with the nature of fuzziness. Improving this incompatibility, in [4], we quoted a revised definition for fuzzy bags based on the proposed definition of bags in [2].…”